Question: A man standing on a road hold his umbrella at 30<sup>0</sup> with the vertical to keep the rain away...

Question

A man standing on a road hold his umbrella at 30⁰ with the vertical to keep the rain away. He throws the umbrella and starts running at 10 km/hr. He finds that raindrops are hitting his head vertically, the speed of raindrops with respect to the road will be

Answer 1

Solution

When the man is at rest w.r.t. the ground, the rain comes to him at an angle 30° with the vertical. This is the direction of the velocity of raindrops with respect to the ground.

Here ${\overset{\rightarrow}{v}}_{rg} =$ velocity of rain with respect to the ground

${\overset{\rightarrow}{v}}_{mg} =$ velocity of the man with respect to the ground.

and ${\overset{\rightarrow}{v}}_{rm} =$ velocity of the rain with respect to the man,

We have ${\overset{\rightarrow}{v}}_{rg} = {\overset{\rightarrow}{v}}_{rm} + {\overset{\rightarrow}{v}}_{mg}$ ......(i)

Taking horizontal components equation (i) gives

$v_{r ⥂ g}\sin 30{^\circ} = v_{mg} = 10km/hr$

or $v_{rg} = \frac{10}{\sin 30{^\circ}} = 20km/hr$